Business Math & Statistics: Exercises and Solutions, Exams of Business Mathematics

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answers/accurate solutions|Already graded A+ x^5 = 32 solve for x - correct answer x = 2 2^x = 16 solve for x - correct answer x = 4 Solve for x and y for these simultaneous equations: 3x = 14-5y 7x+2y = 23 - correct answer x = 3 y = 1 Equation for Total Cost - correct answer Total costs = (variable cost per unit * number of units produced) + Fixed Costs Material $75/television Direct Labor $40/television New Manufacturing Equipment $1,500, Modifications to Factory $3,000, If this company is considering building 10,000 units this year (and needs money for the entire year allotted to it now for this purpose), for how much should the president ask? - correct answer $ 5,650, Contribution Margin - correct answer (price per unit X * # of units sold) - (variable cost per unit X * units sold) Breakeven - correct answer Breakeven = Fixed Costs/Contribution Margin per unit A company is making a product and has invested $100,000 on an advertising campaign and $75,000 each on five salespeople (annual salary, including benefits and support). These are the only fixed costs that the company has assigned to the product, and the contribution margin per unit is $50. To cover those fixed costs, how many units will the company have to sell to breakeven? - correct answer [($75,000*5) + $100,000] / $50/unit = 9,500 (breakeven level in units) abscissa - correct answer The x-coordinate of a point (independent variable) ordinate - correct answer The y-coordinate of a point (dependent variable) True/False: the fixed costs for a certain project are $50 and it costs $2 to produce one unit. The equation that relates y (total costs) to x (total number of units produced) is y = 2 + 50x - correct answer False. It would be y = 50 + 2x

answers/accurate solutions|Already graded A+ Which of the following is the monomial expression? A) 4x^3 + 6x^4 +12x^3 + 45x^4 + B) 143x^4 + 3x^ C) 143x^4 + 78x^4 + 6x^4 + 76 - correct answer B) 143x^4 + 3x^4 - its the only term where the x's can be added together to get one term Write an equation to related total cost to number of driveways paved. Asphalt, tar & concrete/driveway = $7, Direct Labor/Driveway = $12, Office Expenses & Other Labor = $5,000 - correct answer y = 19x + 5 Which of the following is the binomial expression? A) 4x^3 + 6x^4 +12x^3 + 45x^4 + B) 143x^4 + 3x^ C) 143x^4 + 78x^4 + 6x^4 + 76 - correct answer C) 143x^4 + 78x^4 + 6x^4 + 76 - tis the only term where the x's can be added together to get two terms Which of the following is the trinomial expression? A) 4x^3 + 6x^4 +12x^3 + 45x^4 + B) 143x^4 + 3x^ C) 143x^4 + 78x^4 + 6x^4 + 76 - correct answer A) 4x^3 + 6x^4 +12x^3 + 45x^4 +6 - its the only term where the x's can be added together to get three terms True/False: the Contribution Margin is the amount that can be contributed to fixed costs. - correct answer True: the contribution margin is the amount the company receives from the sales of its product minus the product's variable costs. Therefore, the amount remaining (after variable costs) can be used to pay the company's fixed costs. True/False: When the following equation hold true, we are at the breakeven level in dollars: Sales - Variable Costs = Fixed Costs - correct answer True True/False: for the equation 2x - 3y = 6, the x and y intercepts are x=3, y=- 2 - correct answer True When solving for an unknown variable that has a number preceding it, you will divide both sides of the equation by this number, which is known as the: A) base

answers/accurate solutions|Already graded A+ A man buys 3 burgers and 2 jumbo deluxe fries for $7.40. A woman buys one burger and 4 jumbo deluxe fries for $7.80. How much is the burger and how much are the fries? Select one: a. Burger = $1.40, Fries = $1. b. Burger = $1.50, Fries = $1. c. Burger = $2.80, Fries = $2. d. Burger = $2.00, Fries = $2.80 - correct answer a. Burger = $1.40, Fries = $1. True/False: When the following equation holds true, we are not at the breakeven level in dollars: Sales - Variable Costs = Fixed Costs - correct answer False 2x =32, x is a. 5 b. 4 c. 3 d. none of the above - correct answer a. 5 Time Series Analysis - correct answer A forecasting method that uses historical sales data to discover patterns in the firm's sales over time and generally involves trend, cycle, seasonal, and random factor analyses Simple Average - correct answer Found by adding the values of all the data samples and dividing the sum by the number of samples Moving Average - correct answer similar to simple average except that this method only incorporates the most recent data samples Weighted Average - correct answer includes as many data samples as desired and assigns "weights" or measures of importance to each Weighed moving average - correct answer A method of combining the moving average and the weighted average Trend Analysis - correct answer uses past actual values to forecast; however, it is used when there is a noticeable trend over time True/False: When forecasting data that are arranged in time periods, i.e., a time series analysis, there are two different approaches: trend analysis and averaging. - correct answer True When you develop a string of simple averages by adding a data sample at a new time period and drop the oldest data sample, you have a:

answers/accurate solutions|Already graded A+ A) Moving Average B) Simple Average C) Weighted Average D) Trend Analysis - correct answer A) Moving Average If you graphed the data points in a particular time series and a relatively flat, horizontal pattern was observed, the method that should be used to forecast the next point in the series would be: A) a horizontal method B) an averaging method C) a beta method D) a trend analysis method E) none of the above - correct answer B) an averaging method True/False: If the data points in a trend line are plotted on a graph, a trend line can be fitted to the data using the least squares method. - correct answer True. The least squares method attempts to find the line which minimizes the sum of the squared deviations (distances) of the data points to the trend line. in the formula y = a + bx, what is b? - correct answer B is the slope in the formula y = a + bx, what is a? - correct answer a is the y-intercept How do you calculate y in y = a + bx? - correct answer y is the sum of y divided by n How do you calculate x in y = a + bx? - correct answer x is the sum of x divided by n Which of the following statements is false? A) Simple averaging considers all data samples equally B) Using simple averaging when data samples have a lot of variability will provide accurate forecasts C) Simple averaging is easy to understand and apply - correct answer B) Using simple averaging when data samples have a lot of variability will provide accurate forecasts True/False: Allison's time-series data for periods 1 through 7 were used to develop a trend line. She cannot use the trend line to predict a point for period 8 - correct answer False When you develop a string of simple averages by adding a data sample at a new time period and dropping the oldest data sample you have a:

answers/accurate solutions|Already graded A+ a. it's easier to remember. b. it reduces variation. c. it increases accuracy. d. all of the above. e. none of the above. - correct answer d. all of the above. Scatter Diagram - correct answer displays data of two variables. Similar to those done in time series except that the data follows no clear progression through time. True/False: A regression analysis attempts to find the line through a scatter of data points which minimizes the sum of the squared deviations of the points from the line. - correct answer True. The line that minimizes the sum of the squared deviations of the data points from it is referred to as having the best fit. True/False: The coefficient of determination is the unexplained variation divided by the total variation. - correct answer False: it is the explained variation divided by the total variation. True/False: Suppose that two judges, Bill and Ted, each score five competitive divers using a scale from 1 to 10 (with 10 being the best). The correlation coefficient between Bill's and Ted's scores is 1, which means that Bill and Ted gave the divers the same score. - correct answer False. The correlation coefficient measures the strength of a linear relationship between Bill & Ted's scores, not whether one's scores are lower or higher or the same as the other's scores. For example, a correlation coefficient of 1 could be obtained by Ted giving scores of 1,2,3,4, and Bill giving scores of 2,4,6,8,10 to the same divers. True/False: the residual is the difference between the actual value and the predicted value of a dependent variable. - correct answer True: The difference between the Y-value of a data point and the predicted value corresponding to it on the regression line is called the residual. True/False: if r^2 of 0.5 means that as x goes up, y goes down, and vice versa. - correct answer False: r^2 is the coefficient of determination, which tells us how much of the scatter of data points is explained by the regression model. The coefficient of correlation (r) would tell us which way the y would change (increase or decrease) as x changes. Zero-one or dummy variable - correct answer One that cannot be given a numerical value True/False: a correlation coefficient of - 2 means that as x goes up, so does y. - correct answer False: a negative correlation coefficient means that as x increases, y decreases. Also, it is not possible to have - 2 as a correlation coefficient. Susan wants to study the effect of water on the growth of flowers in her garden. She determines a regression line where water is the independent variable (measured in fluid ounces) and flower growth is the dependent variable (measured in cm). If one of her flowers is

answers/accurate solutions|Already graded A+ 40 cm tall, and the regression line is y = 15 + 5x, estimate how many fluid ounces of water it has been given. A) 20 B) 215 C) 5 D) 115 - correct answer C) 5 Plug 40 cm in for y and solve for x. True/False: In a study, the correlation coefficient between class attendance and grades for a group of students was 0.18. Thus 3.24% of the variation in grades was explained by differences in class attendance. - correct answer True. The coefficient of determination is the square of the correlation coefficient. Dependent variable - correct answer The variable the forecaster wishes to predict True/False: Simple regression is made up of one independent and one dependent variable, while multiple regression is made up of one independent and many dependent variables. - correct answer False: multiple regression is made up of one dependent and many independent variables. Edna's T-ratio is less than 2 for the constant term in her regression equation. She should be: A) looking for another set of data since she cannot use this one. B) very concerned. C) not very concerned. D) None of the above. - correct answer C) not very concerned T-statistics less than 2 are an area of concern for the coefficient of the independent variable because they may indicate a zero coefficient. A zero coefficient means there is no relationship between the independent and dependent variables. On the other hand, the constant term has no particular significance to the analyst and can enjoy a low T-ratio. Jamie's regression equation shows a correlation between X3 (the T-ratio is 5) and X4 (The T- ratio is 12) of 0.4. He should: A) throw both variables out B) keep both C) Throw out X3, keep X D) Throw out X4, keep X

answers/accurate solutions|Already graded A+ Which of the following is a dummy variable? Select one: a. fish weight b. fish length c. fish species d. None of these make sense - correct answer c. fish species True/False: A simple regression involves a single independent variable. - correct answer True A coefficient of determination of 0.94 for a regression analysis would indicate Select one: a. 6% of the variation is explained by the regression equation b. 94 % of the variation is not explained by the regression equation c. 94% of the variation is explained by the regression equation d. 6% of the variation is random - correct answer c. 94% of the variation is explained by the regression equation Coefficient of determination = explained variation/total variation, or r^2 = EV/TV A real estate agent says he can approximate the value of a house through the following equation: SP = 125,000 + 3000BR + 500BDR + 4000WC - 6000P; where BR= # of bathrooms, BDR= # bedrooms, WC =Wine cellar and P=Pool. The best selling price estimate for a 3 bedroom, 2 bath house with a wine cellar and pool is Select one: a. $133, b. $132, c. $131, d. $130,500 - correct answer d. $130, A typing instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. Her regression equation looks like: Y' = 11 + 7x1 + 5x2 + 3x3 where: Y' = typing speed in words per minute; x1= hours of instruction per week; x2= hours of practice per week; x3 = hours of typing per week necessary for school or work; A new student is taking 2 hrs of typing instruction per week, will practice 5 hrs per week

answers/accurate solutions|Already graded A+ and must type 2.5 hours per week for work. If the standard error of the estimate is 2, within what range do we have a 95.45% probability that that student's typing speed will be in two months? Select one: a. 53.5 and 61.5 words per minute b. 49.5 and 65.5 words per minute c. 57.5 and 65.5 words per minute d. none of the above - correct answer a. 53.5 and 61.5 words per minute I do not know how to calculate this. A study is being made of the relationship between seniority, i.e., years of service with the company, and the number of workdays absent per year. The following regression line is derived from the data: Days Absent = 9.44 - 1.09(Years Employed) The best estimate of the number of times a 5-year employee will be absent is Select one: a. 8. b. 3. c. 5. d. None of these make sense - correct answer b. 3. I do not know how to calculate this. True/False: A researcher believes, among other things, the town one lives in within the state influences the likelihood of contracting cancer. He has data from three towns and has decided to code the towns as follows X = Town, where: X = 0 if C'burg, X = 1 if B'burg, X = 2 if L'burg. This is an appropriate means for including qualitative data into his analysis. - correct answer False True/False: Unlike regression, trend analysis limits the prediction of the unknown variable to historical levels of the same variable. - correct answer True For trend analysis, its just time-based True/False: Regression limits the prediction of the unknown variable to historical levels of that same variable. - correct answer False Let us imagine that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands (b1), alcoholic beverage sales in $10,000 (b2), and decrease in the price of gasoline in cents (b3). Furthermore, imagine that

answers/accurate solutions|Already graded A+ Kate is an avid bowler. Her bowling scores are normally distributed with a mean of 186 and a standard deviation of 24. She is in a tournament and needs to bowl a 150 or greater for her team to win. If not, her team will lose. What is the probability that her team will win? - correct answer 0. Find the z-score, (150-186)/24 = - 1. Look up +1.5 on the normal distribution probability table in Appendix C and it is 0.06681. 1 - 0.06681 = 0. There are ten balls in a bucket, each a different color. The probability of a blindfolded person randomly choosing the one marked of those ten exactly two out of seven times if the balls were returned to the bucket between drawings is what? - correct answer 0. The probability of choosing that ball one time is 1/10, or 0.10. Looking at the binomial distribution table in Appendix B, match the row that contains two successes (r) and 7 trials (n) with the row that contains the individual probability of success of 0.10 is 0. (Chapter 4, Illustration 4) What is the probability that Kent will catch 3 swordfishes or fewer? - correct answer 0. Add up all the probabilities of 3 swordfish or fewer: 0.1 + 0.2 + 0.35 + 0.2 = 0. True/False: The Bernoulli Trial is an event with two or more possible outcomes. - correct answer False: it only has two possible outcomes True/False: The mean, median and mode are all the same in a normal distribution - correct answer True. the mean of a normal distribution is also the median, since half of the data points fall on each side. The mean is also the most likely outcome (the outcome having the highest probability of occurring), which is why it sits atop the bell-shaped curve; thus, the mean is the mode as well. Suppose we have the normal distribution with a mean of 225 and a standard deviation of 30. Suppose that the z-score for the next sample is 2.5. What is the sample value? - correct answer 300 use the z-score formula. Playing poker, Frank needs the nine of clubs to complete his flush. He accidentally sees that Jim has a club, but didnt see which one. Frank has four clubs in his hand. What is the probability of Jim's card being the nine of clubs? - correct answer 1/9, or 0. There are 13 cards in the suite, and 4 clubs are accounted for. There is only one nine of clubs, so the chances are 1 out of 9 (13-4)

answers/accurate solutions|Already graded A+ What is the probability of flipping a coin three times and each time getting heads? - correct answer 0. Using the Appendix B graph: n = 3 trials r = 3 successes Prob. of Indiv. Successes = 0. If a pea is hidden under one of five nutshells, what is the probability that exactly three times out of five chances that the pea will be correctly discovered? - correct answer 0. Using the Appendix B graph: n = 5 trials r = 3 successes Prob. of Indiv. Successes = 0. See Ch 4 Illustration 5. The farmer wants to know what the probability is of having bags weigh 9 lbs. - correct answer 30.86% Find z-score. (9-10)/2 = 0. See Appendix C chart for 0.5 z-score and 0 is 0.3086, or 30.86% Normal distribution of fastball pitches this season averages at 70 mph and a standard deviation of 4 mph. What is the probability of the next pitch being 80 mph or more? - correct answer 0.621% Find the z-score: (80-70)/4 = 2. See Appendix C chart for 2.5 z-score and 0 = 0.00621, or 0.621% Standard error is calculated the same as... - correct answer standard deviation Formula for standard deviation (and standard error) - correct answer Standard deviation divided by the square root of the number of observations True/False: the type of probability described in the statement "the probability of a randomly selected person having brown hair is 80% if it is a woman" is a conditional property. - correct answer True.

answers/accurate solutions|Already graded A+ True/False: The mode of a probability distribution is the least likely outcome. - correct answer False The mode is the most likely outcome. There are ten ping pong balls in a bucket. Each is equally likely to be picked. If a blindfolded person picks a ball out of the bucket 15 times (the number is noted and the ball is placed back in the bucket each time), what is the probability that the blindfolded person picks the same ball exactly four out of fifteen times(rounded to three decimal places)? Use the Binomial Distribution Probability Table in Ch 4, Appendix B - correct answer 0. n = 15 r = 4 prob of ind. success = 1/10, or 0. Parking spaces at a business school are arranged by a random monthly lottery. There are 3 spaces for every 10 students who want one and all of them have an equal chance of getting one. What is the probability of a student getting a parking space for at least four out of the nine months? (as a decimal) Select one: a. 0. b. 0. c. 0. d. none of the above Use the Binomial Distribution Probability Table in Ch 4, Appendix B - correct answer a. 0. Two independent pollsters surveyed the same number of people from two different populations of approximately equal size. Pollster A concluded he was 95% confident the mean weight of his population is 150 + 16.3 lbs. Pollster B concluded she was 95% confident the mean of her population is 150 + 11.6 lbs. Which of the following statements are true? a. A randomly selected person from Pollster A's population is more likely to weigh between 145 and 155 than Pollster B's population. b. People in the population Pollster A surveyed are less alike in weight than those in the population surveyed by Pollster B. c. The standard deviation of both populations is the same. d. The standard error of both populations is the same. - correct answer

answers/accurate solutions|Already graded A+ The ages of personnel in the accounting department of a large company are normally distributed with a standard deviation of 7 years. There is a 0.02275 probability that the age of any randomly chosen person in the department is less than 22 and 0.15866 probability that the age of any randomly chosen person is greater than 43. What is the mean of this distribution? a. 14 b. 22 c. 36 d. none of the above Use the Normal Distribution Probability Table in Ch 4, Appendix C - correct answer C. 36 Using the z-score equation, solve for mean and look for the probability of the resulting z-score on the table True/False: A distribution that is not a normal distribution does not have a standard deviation - correct answer False A survey among entrepreneurs indicates that the average number of hours worked per week is normally distributed with a mean of 60 hours and a standard deviation of 15 hours. What is the probability that the next entrepreneur surveyed will work less than 30 hours per week? (as a percentage, to three decimal places) a. 2. b. 0. c. 2. d. none of the above Use the Normal Distribution Probability Table in Ch 4, Appendix C - correct answer a. 2. Suppose a population numbers in the millions. If one takes a random sample from that population of an appropriate size to meet normality assumptions, the mean of the sample will be the same as the mean of the population. a. always true b. always false c. may be true, but unlikely d. may be false, but unlikely - correct answer c. may be true, but unlikely

answers/accurate solutions|Already graded A+ Event node - correct answer represented by circles on a decision tree; represents points of uncertainty where one of two or more things will happen that are out of the control of the decision maker How do you use bracket medians to evaluate continuous uncertainty? - correct answer Assess the 0.1, 0.3, 0.5, 0.7 and 0.9 fractiles of the range of uncertainty for your outcome, and then multiply the values at each of those fractiles by the probability of 0.2. Add up each of the products and your sum will be the expected monetary value of your outcome. How do you use the Pearson-Tukey Method to evaluate continuous uncertainty? - correct answer Assess the 0.05, 0.5, and 0.95 fractiles and then multiply by the values found at each of those fractiles by probabilities of 0.185, 0.63, and 0.185, respectively. Add up each of the products and your sum will be the expected monetary value of your outcome. A band of treasure hunters is trying to determine whether eighteenth-century pirates buried any treasures on a small island. They figure that if they find any signs of early settlement on the island that there is a good chance that treasure is buried there. Which of the following represents the left-most event or decision node on the treasure hunter's decision tree? A) Pirates bury or do not bury their treasure B) Treasure hunters find or do not find signs of settlement C) Settlement was or was not built D) None of the above - correct answer B) Treasure hunters find or do not find signs of settlement Which of the following would be best represented by a decision node? A) Bob rides a cab or a bus to work;, whichever he can find the most quickly B) Sal either wins or doesn't win the lottery C) Jill goes to work for one of two firms who have offered her a position D) None of the above - correct answer C) Jill goes to work for one of two firms who have offered her a position A local artist has three civic buildings, one of which she wants to paint. If she paints any of these buildings, she can sell the painting to the organization that occupies the building, sell the paining to a private collector or donate it to a small museum. The order for the decision tree would follow which way? A) decision node, event node B) event node, decision node, event node

answers/accurate solutions|Already graded A+ C) event node, event node, D) None of the above - correct answer D) None of the above It would actually be decision node (which building to paint), decision node (what to do with the painting) True/False: the Expected Monetary Value (EMV) is a number based on averaging - correct answer True Marcie wants to invest her money in the stock of one of two companies: Writeoff, a maker of erasers, or Outatwon Books, a publisher of travel guides. She has a 0.7 probability of making $10,000 and a 0.3 probability of losing $25,000 with Writeoff stock, and a 0.45 probability of making $3000 and a 0.55 probability of losing $500 with Outatown Books stock. If she does nothing, she will neither gain nor lose money. Should she invest in Writeoff stock, Outatown stock or do nothing? - correct answer Invest in Outatown stock Referring to Illustration 9 in Chapter 5, it shows the decision tree for three projects in which the AOK company can invest (they can only invest in one and must invest). In which one of the three projects should AOK invest, based on EMV? A) Project A B) Project B C) Project C D) None of the above, they are all equal. - correct answer C) Project C True/False: the EMV of an alternative with 0.5 probability of making $500 is definitely $250. - correct answer False You cannot calculate the EMV with just this information. You need to know all possible returns, not just one.All possible outcomes should equal one, but you only have 0.5 of the information required. Which of the following nodes could be combined into one? A) If Jay decides to go to lunch, he has to decide where to go B) After Jay decides to go out to lunch, he has to make sure he doesnt have a meeting and, if he doesnt, he has to decide where to go out to lunch C) Jay finds out whether he has a meeting, then he will decide D) None of the above - correct answer A) If Jay decides to go to lunch, he has to decide where to go